19.3.23 Linear Operators

Condition: Prove that the operator \ (a: c [0.1] \ rightarrow c [0.1] \), \ ((a x) (t) (t) (t)+\ lambda \ int_ {0} {1} E^{s+t} x (s) d s \ quad \) has a limited reverse operator \ ( A^{-1} \) and find it.